Data communications in many systems is done with data packets consisting of control information and payload data. The control information and/or the payload data usually includes a plurality of data symbols. To simplify receiving operations and provide for robust data communications, many systems break up the frequency-selective communication channel into a number of flat (e.g., non-frequency-selective) channels and communicate data simultaneously on multiple subcarriers. A common example is a system that uses orthogonal frequency division multiplexing (OFDM). In OFDM systems, a data symbol consists of data on multiple sub-carriers for that data symbol. Some sub-carriers may carry payload data, and some sub-carriers may be used for pilot tones, which carry known data (e.g., training data known to a receiver and transmitter of the communication system).
Data packets communicated over communication systems incur distortion introduced by the communication system due to device implementations and environmental factors. For instance, oscillators in transmitters and receivers of the communication system (e.g., used to upconvert or downconvert a signal for transmission or reception, respectively) introduce phase noise. In another example, gains of power amplifiers used by transmitters of the communication system often exhibit changes over time (e.g., gain drift). The distortions caused by phase noise and amplifier gain drift manifest as a common phase error to the subcarriers of a data symbol in an OFDM system. For instance, a common, or same amount of phase error is introduced to each of the subcarriers of a data symbol of the data packet by the phase noise or amplifier gain drift. The common phase error can degrade a receiver's decoding capabilities, such as by increasing a packet error rate (PER) measure in the receiver to the point where the data is not recoverable and consumable by a user.
Consequently, a receiver estimate a common phase error of a data symbol and apply appropriate compensation, such as when extracting data or adjusting receiver synchronization. An estimate of common phase error term is often determined from pilot tones of a data symbol and used to estimate payload data in the data symbol, without including pilot tones from other data symbols in the data packet when estimating common phase error. However, because the number of pilot tones in a data symbol in some protocols can be small, the estimate obtained by such traditional methods is often poor, and errors are introduced. Moreover, when the signal-to-noise ratio (SNR) of the data packet is low (e.g., due to low signal strength, noisy circuits, or combinations thereof), relying on pilot tones from one data packet can yield poor estimates of the common phase error. Furthermore, methods that determine an estimate of common phase error by restricting the estimate to one data symbol are sub-optimum, because they do not exploit the coherency of oscillator phase noise or amplifier gain drift that is often not limited to the duration of one data symbol in an OFDM system.